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Floats in a Network

Updated on March 28, 2012


This is in continuation of a hub: Case Study: PERT/CPM – calculating floats. Some terms used in the said hub would be repeated for a complete understanding of the concepts and techniques.

A float is a slack or cushion or flexibility or margin for delay. It shows time available for delaying an activity without delaying the Project. It would not result in either increase in duration or cost of the project.

For calculating floats, there are different Methods depending upon format of the Network used. There are two types of Net Works: Activity-On-Node (AON) and Activity-on-Arrow (AOA). Results are same in both cases.

In this hub, only network based on AON would be used.


What is a Node?

Node means box or bud or bulge or knob. In network, such a node is represented by a square normally divided into 9 sectors. These can be increased or decreased as per convenience or requirements. It is not necessary to fill in all the cells or compartment but some can be left empty for any future reference. Each node contains information like Project Description, Project ID, its duration, early start and finish, late start and finish and floats like free float & Total Float. This is shown in the side sheet.


To calculate float, an example of Desert Hospital is being given. It has thirteen activities which are shown along their duration in weeks and precedence.


A project network is a graph showing the sequence in which project activities would be completed. It is event-oriented technique not just showing start and finish but the way, the activities are linked together and the manner in which these are to be carried out. It is applied to large-scale, one-time, complex, non-routine projects.

The network technique was first developed by Frederick Taylor and later refined by Henry Ford . DuPont Corporation's CPM was developed at the same time.

From the data given in the question, the following network is drawn. Necessary steps have been discussed in the earlier hub on Float.

Network without floats

Portion of Network

Float Calculation


Floats or slacks are only available in non-critical activities shown linked by blue lines.

To start with two types of floats would be calculated: (i) Free Float (FF) and (ii) Total Float (TF).


The FF indicates maximum delay from early start of an activity without delaying the earliest start of any of its immediate successor activities. The formula is: FF = ES of immediate succeeding Node (or activity) minus ES start of existing Node minus its duration. It can be shortened to ES of immediate succeeding Node minus EF of the exiting Node. If there are more than one succeeding Nodes, minimum would be the Free Float of the existing Node.

In the side sheet, F has only one succeeding Node, H. Hence ES of H, 7 minus EF of F would be equal to Zero.

E is succeeded by two Nodes i.e. J & K. Therefore, FF would be minimum of the two as shown below:

FF for Node E:

  • ES of J – EF of E = 10 – 7 = 3 or
  • ES of K – EF of E = 10 – 7 = 3,
  • Therefore, FF for E = 3

Likewise FF for Node H would be:

  • ES of J – EF of H = 10 – 10 = 0 or
  • ES of K – EF of H = 10 – 10 = 0,
  • Therefore, FF for H = 0


TF refers to maxim flexibility or margin available for delaying an activity. Here an activity can be started as early as possible and finished as late as possible. Therefore it would provide more flexibility.

Its calculation is easy. For a Node touched by only one tail, it would be difference between EF and LF of the same Node.

TF for E:

  • LF of E– EF of E = 12 – 7 = 5

TF for H:

  • LF of H – EF of H = 12 – 10 = 2 or


Constructin of a Mega Project


Three more floats would be discussed now:

  1. Independent Float
  2. Interference Float
  3. Safety Float


  • Shows the time available even if an activity has a Late Start and Early Finish.
  • the delay possible for an activity if all preceding activities start as late as possible whilst all subsequent activities start at their earliest time
  • It is most adverse type of float and often results in a negative figure.

In case of Node F, its EF = 7, while its LS=5 and duration is 4. So Independent Float would be 7 - 5 -4 = -2 or Zero which is higher. In other words, if this float is in negative, it is to be shown as zero float or no float.


There are two versions of Interference Float.

In the first version, it is like manipulation and it is calculated as Interference Float = TF – Independent Float. While Independent Float is available in all cases, Total Float is available only if an activity is started at its earliest and finished at the latest time. The difference between the two shows the extent to which one can avail margin or flexibility.

Second version is the reduction, total float can bring in the next succeeding activities and is represented by TF – FF.

As per first version, the Inference Float for activities 'F' would be TF - Ind. Float or 2-0 =0. In the second version, it would remain 2 (TF - FF or 2 - 0 = 2) as incidentally both Free Float and Independent Float are zero.


The SF of an activity is the leeway for scheduling, all its predecessors without affecting its self. It is calculated as:TF + Int F = FF + SF. One can find out SF, when all other relevant floats are available. (This float is not so popular. It was introduced by Thomas W in his article "Four Floats Measures for critical Path Scheduling."


Critical Path Method 
Project Evaluation & Review Technique 
Activity On Node 
Activity On Arrow 
Critical Activities
Activities having no flexibility or margin for delay
Dummy Activities
Not a real activity but only a link
Total Float
Maximum cushion based on early start and late finish
Independent Float
Minimum float available in any case
Free Float
Normal float based on early start and early finish


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    • profile image

      Mr Muyungi Melcher 

      5 years ago

      thanks a lot

    • hafeezrm profile imageAUTHOR


      5 years ago from Pakistan

      It is LS - EF - Duration = Independent Float is correct. I am looking for a suitable example and would revert to when I found one.

    • profile image


      5 years ago

      Hi, Thanks for the interesting article.

      My question is that there is contradiction in the Independent float definition between this article and your article below:

      where here it states IF=EF-LS-D

      In the other one it's IF=EF-LS only (CALCULATIONS OF FLOATS UNDER AON section)

      Which one should we use?


    • profile image


      6 years ago

      Really transparent and vivid explanation............................................................thank you

    • profile image

      Mawanda Tonny Joseph 

      6 years ago

      nice article

    • profile image


      6 years ago

      thnks it helped me.........:D

    • profile image

      mustapha bello k.k 

      6 years ago

      i thank you so much sir, i am writing my exams tomorrow,

    • hafeezrm profile imageAUTHOR


      6 years ago from Pakistan

      Thanks Annie. God bless you.

    • profile image


      6 years ago

      Thanks sir. You are a great teacher. you create lot of interest to learn with simple and clear method.

    • hafeezrm profile imageAUTHOR


      6 years ago from Pakistan

      Independent Float (IF) is difference between Early Finish (EF) and Late Start (LS). As it is available in all cases ( does not depend upon Early Start (ES) or Late Finish ( LF).

      The Interfering Float (INT F)has two versions (i) Total Float (TF) - IF and (ii) TF - Free Float (FF).

      "IF " is the minimum possible float while Interfering Float is the extent to which one has a leeway or possibility of interference.

      You may make a model to understand this problem. ES =12, LS=14, Duration 5, EF=20 & LF=25.

      If there is still some confusion, please do not hesitate to contact.

      I have been to Pokhara and enjoyed scenery of Fish Tail, Phewa Lake, RadhaKrishna Temple and Water Falls.

    • profile image

      Narayan Timilsena 

      6 years ago

      I teach Construction Project Management of Pokhara University course. This is helpful for me but i am confused in the relation between independent float and interfering float............

    • Rana Mohsin Alyas profile image

      Rana Mohsin Alyas 

      7 years ago from karachi.......

      i learn today in class........and now furthr read here. now i can say that i understand very much by this hubs....thank you sir..

    • hafeezrm profile imageAUTHOR


      7 years ago from Pakistan

      Thanks Kamran, Asad Ayub and Zohaib for your comments.

    • profile image

      zohaib noor ullah 

      7 years ago

      now i am able to understand total and free float .thank you very much sir

    • asadayub profile image


      8 years ago

      Dear Sir, this article on Float is also a really comprehensive one. it added to my knowledge a lot.I know about Free Float and Total Float but now i'm able to understand the concept of more kinds of Floats.Thank You so much Sir.

    • profile image


      8 years ago

      a very well explained article.thnx

    • hafeezrm profile imageAUTHOR


      8 years ago from Pakistan

      Thanks Mr. Alamgir Khan for your interest.

      There is a missing link. Activity E is preceded by two activities, B & D. (Please see the question).

      Free Float of D should be zero as it is already on the critical path.

      Thanks for pointing out these lapses.

    • profile image

      Alamgir Khan 

      8 years ago

      There seems a type as well in the free float of Activity D. It should be 0 instead of 4. Thanks.

    • profile image

      Alamgir Khan 

      8 years ago

      I think there is an error in ES of Activity E. Should not it be 2 instead of 6? Can you please explain?

    • hafeezrm profile imageAUTHOR


      8 years ago from Pakistan

      Thanks Mr. Alamgir Khan for your kind comments. I have written some hubs on Financial Analysis as well. Just to see kind click:

    • profile image

      Alamgir Khan 

      8 years ago

      I teach at College of the North Atlantic, Canada. For one of my courses namely Project Management and Financial Analysis, I was looking for supplementary material on project float and luckily found this web site. The way this float information is presented here is very interesting and also informative. I thank you for posting such a great deal of material.

      Thank you.

    • aneela Shafi profile image

      aneela Shafi 

      9 years ago

      sirrrr thankyou so much for thoroughly explaining floats all my concepts are cleared now :) thankyou so much for imparting us with your immense knowledge it will help me a lot for the mid terms JazakAllah

    • profile image

      Adnan Ahmed 

      9 years ago

      THANX ALOT SIR ....


    • asif jamal profile image


      9 years ago from Islamabad

      its nice to see ur work on the hubpages and provid us the latest information regarding the project and new thories of the modrn world.

      sir its best way to serve life for education and bettrmnt of the studnt and socity

      sir me thnkful to u that u gve me oppertunty to understand the FLOAT through colorful slides & such kind of informative data

    • profile image

      Sana Karim 

      9 years ago

      Dear Sir,

      This hub is explained in much more detail along with sketches, which has cleared all my concepts regarding FLOATS.

      Thank you so much sir for providing us that much knowledge.


    • profile image

      hira sami 

      9 years ago

      this is very informative all my doubts are cleared sir thanku v much


    • hafeezrm profile imageAUTHOR


      9 years ago from Pakistan

      Thanks Rufi for your continued interest.

    • Rufi Shahzada profile image

      Rufi Shahzada 

      9 years ago from Karachi

      Dear Sir,

      This HUB is a perfect summary of FLOATS that we have learned in your Lectures.




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